AD-Am 3t4 AD J TECHNICAL REPORT ARLCB-TR-81008 TECHNICAL LIBRARY A PHOTOELASTIC STUDY OF STRESSES IN SINGLE-GROOVE CONNECTIONS OF THE SAME MATERIAL Y. F. Cheng February 1981 US ARMY ARMAMENT RESEARCH AND DEVELOPMENT COMMAND LARGE CALIBER WEAPON SYSTEMS LABORATORY BENE'T WEAPONS LABORATORY WATERVLIET, N. Y. 12189 AMCMS No. 6111.01.91A0 PRON No. 1A1281501A1A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED Dnc QUALmr INSPECTED a
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A PHOTOELASTIC STUDY OF STRESSES IN SINGLE-GROOVE ... · The photoelastic data, i.e., the fringe orders and isoclinic parameters, were measured by means of a photometer (Photovolt
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AD-Am 3t4
AD J
TECHNICAL REPORT ARLCB-TR-81008 TECHNICAL LIBRARY
A PHOTOELASTIC STUDY OF STRESSES IN SINGLE-GROOVE
CONNECTIONS OF THE SAME MATERIAL
Y. F. Cheng
February 1981
US ARMY ARMAMENT RESEARCH AND DEVELOPMENT COMMAND LARGE CALIBER WEAPON SYSTEMS LABORATORY
BENE'T WEAPONS LABORATORY
WATERVLIET, N. Y. 12189
AMCMS No. 6111.01.91A0
PRON No. 1A1281501A1A
APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED
Dnc QUALmr INSPECTED a
DISCLAIMER
The findings in this report are not to be construed as an official
Department of the Army position unless so designated by other author-
ized documents.
The use of trade name(s) and/or manufacturer(s) does not consti-
tute an official indorsement or approval.
DISPOSITION
Destroy this report when it is no longer needed. Do not return it
to the originator.
SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)
REPORT DOCUMENTATION PAGE 1. REPORT NUMBER
ARLCB-TR-81008
2. GOVT ACCESSION NO,
4. TITLE (and Subtitle)
A PHOTOELASTIC STUDY OF STRESSES IN SINGLE- GROOVE CONNECTIONS OF THE SAME MATERIAL
7. AUTHORfaJ
Y. F. Cheng
READ INSTRUCTIONS BEFORE COMPLETING FORM
3. RECIPIENT'S CATALOG NUMBER
5. TYPE OF REPORT & PERIOD COVERED
6. PERFORMING ORG. REPORT NUMBER
8. CONTRACT OR GRANT NUMBERCs.)
9. PERFORMING ORGANIZATION NAME AND ADDRESS
US Army Armament Research and Development Command Benet Weapons Laboratory, DRDAR-LCB-TL Watervliet, NY 12189
10. PROGRAM ELEMENT, PROJECT, TASK AREA 4 WORK UNIT NUMBERS
AMCMS No. 6111.01.91A0 PRON No. 1A1281501A1A
If. CONTROLLING OFFICE NAME AND ADDRESS
US Army Armament Research and Development Command Large Caliber Weapon Systems Laboratory Dover, NJ 07801
12. REPORT DATE
February 1981 13. NUMBER OF PAGES
30 14. MONITORING AGENCY NAME ft ADDRESSC/f di/Zarent from Controlling Oflice) 15. SECURITY CLASS, (of thla report)
UNCLASSIFIED 15a. DECLASSIFI CATION/DOWN GRADING
SCHEDULE
16. DISTRIBUTION STATEMENT (of thla Report)
Approved for public release; distribution unlimited.
17. DISTRIBUTION STATEMENT (of the abatracl entered fn Block 20, If different from Report)
18. SUPPLEMENTARY NOTES
19. KEY WORDS (Continue on reveree aide It necessary and Identify by block number)
Groove Connections Photoelastleity Maximum Fillet Stresses Contact Stresses Stress Concentrations
20. ABSTRACT fCbcrtioua «a revwrme sidm ff neceaaary and Identify by block number)
This report describes a three-dimensional photoelastlc study on stresses in single-groove connections of the same material. Two groove profiles were investigated; namely, the British standard buttress and the new profile. Boundary stresses, interior stresses, and contact stresses were determined. Shear-difference method was used and the procedure of the method was outlined.
(CONT'D ON REVERSE)
DD , FORM JAN 73 1473 EDITION OF » MOV 65 IS OBSOLETE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Dale Entered)
SECURITY CLASSIFICATION OF THIS PAGE(T»7i«n Dmta Bntand)
20. Abstract (Cont'd)
Appropriate checks for the accuracy of the results were made. Heywood's empirical equation for calculating maximum fillet stress In loaded projections was reviewed. It was found that the British standard buttress is stronger than the new profile and that the Heywood's equation is not applicable in our problem. Further work on multi-groove connection is in progress.
SECURITY CLASSIFICATION OF THIS PAGEflWion Data Entered)
The three-dimensional shear-difference sub-slice method was developed by
Frocht and Guernsey^'5 in 1952. For the sake of completeness of this report,
a brief outline is given here. The necessary and sufficient photoelastic
data, i.e., the fringe orders and isoclinic parameters, for the complete
determination of stresses along a given line are obtained from a sub-slice
having the form of a parallelopiped, the axis of which is the given line of
interest. Figure 4(a). The shearing stresses TyX and TZX on the four
longitudinal sides, Figure 4(b), are determined from four observations at
normal incidence: I4, L3, L4, and L5. For example,
1 Tyx = - (p'-q^sin 2<j)' (1)
^Frocht, M. M. and Guernsey, R. Jr., "Studies in Three-Dimensional Photoelasticity - The Application of the Shear-Difference Method to the General Space Problem," Proceedings First US National Congress of Applied Mechanics, pp. 301-307, December 1952.
5Frocht, M. M. and Guernsey, R. Jr., "Further Work on the General Three- Dimensional Photoelastic Problem," Journal of Applied Mechanics, Trans. ASME, Vol. 77, No. 2, pp. 183-189, June 1955.
where p' and q' are the secondary principal stresses* at a point in the
xy-plane obtained from normal incidence in the z-direction, and (f)' is the
corresponding isoclinic parameter. Similarly
1 Tzx = " Cp"-q,,)Bln 2<r (2)
where p" and q" are the secondary principal stresses at a point in the xz-
plane obtained from normal incidence in the y-direction, and $" is the
corresponding isoclinic parameter. Knowing TyX and TZX, it is possible to
determine an approximation to the partial derivatives 9TyX/9y and 8TZX/3Z.
Thus
(3Tyx/3y)Xiy>z - (ATyx/Ay)Xjy)Z
= [(Tyx)x,y+(Ay/2)>z " (Tyx)x,y-(Ay/2).zl/Ay (3a)
OTzx/3z)x>y>z « (ATzx/Az)Xjy)Z
= [(Tzx)x>y,z+(Az/2) " (Tzx)x,y,z-(Az/2)]/Az (3b)
where the subscripts denote the coordinates of the points where the shears are
evaluated.
*The secondary principal stresses for a given direction are the principal stresses resulting from the stress components which lie in a plane normal to the direction. Thus the secondary principal stresses p' and q1 for the z- direction are the principal stresses resulting from the stress components ax, ay and Txy and p'.q' = (l/2)(ax+ay) ± {[(1/2)(ax-ay)]
2 + Txy2}l/2. The other
stress components which lie in a plane parallel to the given direction have no photoelastic effect when observed along the direction.
Knowing ATXy/Ay and ATZX/AZ, it is possible to determine approximately
the stress ax at any point on the x-axis, i.e., the line of interest. From
the first differential equation of equilibrium without body forces
3ax/8x + 8-ryx/3y + 3TZX/3Z = 0 (4)
we obtain, upon integration and substitution of finite differences, the
expression i 1
(Ox)i = (ax)o " I (Aiyx/AyMx - I (ATZX/AZ)AX (5) o o
where the subscript o denotes the starting point at the boundary having a
known initial value of ax and the subscript 1 denotes any interior point on
the axis.
Once (ax)i is known, the remaining normal stresses (ay)i and (az)i can be
computed from the following equations:
(ay)i = (ax)l " (p'-q^cos 2$' (6a)
(o^i * (ox)i - (p'^q'^cos 2(j)" (6b)
The remaining shearing stress TyZ can be determined from an observation
at oblique incidence: LQ, Figure 4(a) and is given by the equation
Tyz = (Fene s:i-n 2(j)Q - TyX cos 9)csc 6 (7)
where 6 is the angle of incidence of the oblique ray LQ, FQ the model fringe
value in shear, (J>Q the isoclinic parameter, and ng the fringe order for the
oblique path.
EXPERIMENTAL RESULTS
Fillet Boundary Stresses
Figures 5(a) and 5(b) show the stress patterns of meridian slices from
the first and second models, respectively. It can be seen that in both models
the fringe orders at the free fillet boundary in the outer piece are
considerably less than those in the core. On the free boundary one of the
principal stresses is identically zero, and the remaining principal stress
tangent to the boundary is given by the fringe order. Figures 6(a) and 6(b)
show the free fillet boundary stress. Of, in the core of the first and
second models, respectively. In the first model, the boundary stress has a
maximum value of (af)niax = 61 psi and is located approximately 21 degrees from
the narrowest section, measured toward the loaded surface. In the second
model, (of)max 'ias a value of 98 psi and is located approximately 43 degrees
from the narrowest section, measured toward the loaded surface. This value is
almost 60 percent greater than that of the first model while their loads are
practically the same.
Radial Distribution of Stresses qr, az.y and xvz on the Narrowest Section of the Core
In a r9z-cylindrical coordinate system, equation (5) takes the following
form i i
(0^! = (ar)0 - I (ATzr/AZ)Ar - I (ATer/Ae)Ar (8) o o
For an axially symmetric problem, TQr = TQZ = 0, equation (8) reduces to
1 (OjOi = (or)0 - I (ATzr/Az)Ar (9)
where (ar)0 is the value of ar at the starting point, and Tzr Is obtained by
making photoelastlc observations of the meridian slice at normal incidence to
the rz-plane. Once (or)^ is known, (.az)i can be computed from photoelastlc
relations similar to equation (6).
For a complete determination of the state of stress, the remaining normal
stress OQ can be obtained by preparing a sub-slice from the meridian slice.
This sub-slice has the form of a parallelopiped and its axis is the given line
of interest, the radial line. An observation at normal incidence to the
re-plane along the z-direction, together with a photoelastlc relation similar
to equation (6), yields the normal stress OQ. However, due to the Interest of
preserving the meridian slices, the sub-slice has not been prepared and OQ has
not been determined.
Figures 7(a) and 7(b) show the radial distribution of stresses ar, az,
and Trz on the narrowest section of the core of the first and second models,
respectively. As would be expected, in both models the maximum of az occurs
on the root of the groove Indicating the notch effect. In the first model,
(0z)max has a value of 54 psl, in the second model, 42 psi. They are less
than (af)max in both models.
Stress Concentration Factors
We will define stress concentration factors Kz, Kp, and Kg as follows:
Kz = (of)max/(p/Az) (10a)
Kp = ((Jf)raax/(P/Ap) (10b)
Ks = (0f)max/(p/As) (10c)
where P is the applied load, Az the narrowest cross sectional area, Ap the
shearing area along the pitch circle, and As the shearing area along the
circle of the groove root. The results are shown in Table I.
TABLE I. STRESS CONCENTRATION FACTORS
Model 1 Model 2
Loads, Pounds 59.1 58.8
(af)max. Psi 61 98
! Az, sq. in. (Tr/4)(2.388)2 U/4)(2.328)2 |
Kz 4.6 7.1
' Ap, sq. in. ir(3)(l/2) -
1 Kp 4.9 -
1 As, sq. in. Tf(2.388)(l) n(2.328)(l)
1 Ks 7.7 12.2 |
Contact Stresses
In the determination of contact stresses, a nQt orthogonal coordinate
system was used, in which n was the direction perpendicular to the contact, 9
the circumferential direction, and t the tangential direction. Equation (5)